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Masteriza [31]
3 years ago
6

A particle moves on a straight line and has acceleration a(t)=24t+2. Its position at time t=0 is s(0)=3 and its velocity at time

t=0 is v(0)=13. What is its position at time t=5?
Mathematics
1 answer:
user100 [1]3 years ago
3 0

Answer:

It's position at time t = 5 is 593.

Step-by-step explanation:

The velocity v(t) is the integral of the acceleration a(t)

The position s(t) is the integral of the velocity v(t)

We have that:

The acceleration is:

a(t) = 24t + 2

Velocity:

v(t) = \int {a(t)} \, dt = \int {24t + 2} \, dt = 12t^{2} + 2t + K

K is the initial velocity, that is v(0). Since V(0) = 13, K = 13

Then

v(t) = 12t^{2} + 2t + 13

Position:

s(t) = \int {s(t)} \, dt = \int {12t^{2} + 2t + 13} \, dt = 4t^{3} + t^{2} + 13t + K

Since s(0) = 3

s(t) = 4t^{3} + t^{2} + 13t + 3

What is its position at time t=5?

This is s(5).

s(t) = 4t^{3} + t^{2} + 13t + 3

s(5) = 4*5^{3} + 5^{2} + 13*5 + 3

s(5) = 593

It's position at time t = 5 is 593.

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The probability a randomly selected household owns corporate stock is 0.54. The probability a randomly selected household has no
34kurt

Answer:

30% probability a randomly selected household has no Internet access given the household owns corporate stock

Step-by-step explanation:

I am going to say that we have two events.

Event A: Owning corporate stock. So P(A) = 0.54.

Event B: Having no internet access. So P(B) = 0.3.

Since they are independent events, we can apply the conditional probability formula, which is:

P(B|A) = \frac{P(A \cap B)}{P(A)}

In which

P(B|A) is the probabilitty of event B happening given that A happened. We want to find this.

P(A \cap B) is the probability of both events happening.

Since they are independent

P(A \cap B) = P(A)P(B) = 0.54*0.3

So

P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.54*0.3}{0.54} = 0.3

30% probability a randomly selected household has no Internet access given the household owns corporate stock

8 0
3 years ago
Determine whether the statement is always true, sometimes true, or never true. Give an example. (a) Both sides of an equation ca
arsen [322]

Answer:

(A) Always true

(B) Seldom true

Step-by-step explanation:

(A) Both sides of an equation can be multiplied by the same number without this action changing the solution of the equation.

Keyword here is "number".

Multiplying both sides of an equation by an equal quantity (same number) will result in same solution after solving for the unknown in the equation. This is because that numeric quantity can always be removed by dividing both sides of the equation by it or by a factor (or multiple) of it.

EXAMPLE:

For a linear equation, 4x - 6 = 15x

let's find the solution, in other words solve for the unknown value X.

4x - 15x = 6

-11x = 6

x = -6/11

Now multiply both sides of the equation by 3.

3(4x - 6) = 3(15x)

12x - 18 = 45x   ___new equation

Solve for X

12x - 45x = 18

-33x = 18

x = -18/33

Reduce the fraction to its simplest form by looking for a number that can divide both numerator and denominator without remainder. In other words, think of a number that is a factor of 18 and a factor of 33.

That common factor or highest common factor (HCF) is 3.

Go ahead and reduce the fraction.

x will be reduced to -6/11

(B) Both sides of an inequality can seldom be multiplied by the same number, without such action changing the solution set of the equation.

Inequalities are more complex. Operational signs even change sometimes, in the course of finding the solution set of the inequality.

Sometimes, multiplying both sides of an inequality by a given numeric quantity will change its solution set and sometimes, it won't.

5 0
3 years ago
What is the equation of the line in point slope form given a slope of -3 and a point of (-2,-5)?​
Lelu [443]

Answer:

y = -3x - 11

Step-by-step explanation:

Use the given slope and point in the point-slope equation. Solving this will give us the y-intercept equation.

Point-slope formula: y - y = m(x - x)

Plug in the slope and point

y - (-5) = -3(x - (-2))

Subtracting negatives will make them positive. Multiply out the -3 to what is in the parentheses.

y + 5 = -3x - 6

Subtract the 5 from both sides

y = -3x - 11

The equation of the line is y = -3x - 11

7 0
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List 2. 25%, 14%, 14%. This is not from least to greatest, either.
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List 4. 140%, 14%, 25%. This is not from least to greatest.

List 3 is from least to greatest. I got this answer by converting all of the fractions and decimals to percentages.
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2 years ago
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Leno4ka [110]

Answer: Annie will have to make 228 cookies

explanation:

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5 0
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